These periodic trends in 1st ionisation energy (I.E.) are always the result of more than one factor changing. The most important factors are:
- The effective nuclear charge (Zeff) that the valence electron being removed experiences (roughly equal, for s and p blocks, to the number of valence electrons)
- The potential energy of the sublevel (1s, 2s, 2p etc) that the electron is being removed from
- Any electron-electron repulsion that the electron being removed experiences in its orbital
As we move left to right across the period, factor 1 increases and this dominates the overall shape shown in the graph. A drop occurs from Be to B as we move to the higher potential energy 2p orbital (so the electron is easier to remove) and this is more important than the increasing Zeff from 2+ to 3+. As we move to C, the Zeff increases to 4+, so it has a higher I.E. than B (same sublevel, 2p).
The reason that C's I.E. is higher than Be also is because the change in Zeff from Be to C is +2 to +4 (it roughly doubles) and this is more important than the difference in potential energy between the 2s and 2p sublevels, so factor 1 takes over again, over factor 2.
I haven't discussed factor 3. Anytime an electron is removed from a paired orbital, it is a little easier (lower I.E.) than exactly the same situation (same Zeff, same sublevel potential energy) from an unpaired orbital, due to electron-electron repulsion within the paired orbital. It is a small factor between Be and C (Be is a paired 2s, C is an unpaired 2p) but it is very minor compared to factors 1 and 2 changing between these species, so C is still harder to remove.
It is tempting to say that a filled sublevel, or orbital, is "stable" = higher I.E. This statement comes not from the fact that the sublevel is full (these paired electrons are actually easier to remove than you would expect, due to electron-electron repulsion) but because filled sublevels always correspond to the highest Zeff for that sublevel.
You can employ these arguments to explain all the trends in the simple (s and p block) 2nd and 3rd periods. Things get much more complicated in other parts of the table!